Solo (without an accent): Lonely, alone, without some one else.
'Estoy solo en casa' (I'm home alone).
Sólo (with accent): Only, just.
'Sólo quiero estar en casa' (I just wanna be home).
Único: unique, also can be translated as only in some cases.
'Una pieza única' (A unique piece).
'Es mi único amigo' (He's my only friend)
Best regards,
Alejo.
REF.: I'm a Spanish Teacher.